Given your requirements, any controller with a way to communicate with the Bluetooth module and a single I/O pin can control 100 LEDs.
If, however, you want individual control of each LED, that changes things. If the LEDs are RGB LEDs, that changes things. I think you can see where I'm going here: without specifying your requirements well, you do not limit your choices by any considerable amount.
Odds are that it won't be a single controller that will drive each LED (notice I said drive, not control), meaning that there are ways to control it without using a fast/big/expensive controller.
Say, for instance, you decide to use 13 cascaded shift registers, then, depending on controls needed for them, you could control 100 LEDs using 3 I/O pins, making a small, 8 pin microcontroller (possibly) more than enough for your application.
What kind of refresh rate are we talking here? How often do you want all LEDs to be able to respond to a frame/command?
Again, the longer it takes for you to specify your requirements, the longer and more dragged out this process will be...
if you can have somme mS delay , beetween commande of each groupe, you can
command 96 leds with 6 MCP23017 on I2C bus ,
16-Bit I/O Expander with Serial Interface
each can command 16 outputs
after maybe you have to add power driver like ULN3008
because , all output active => 125mA maxi into VDD pin
<8mA/output